Approximate Analytical Model Research Articles

Approximate analytical model of the refracted field of the Gaussian light beam on a plane dielectric interface

An approximate two-dimensional analytical model is proposed for description of a stationary monochromatic field arising at the Gaussian light beam refraction into a transparent or weakly absorbing homogeneous medium. Its formulae describe the spatial structure of a refracted field in a wide range of variation of incidence angles, when this field is characterized by free propagation, total internal reflection, or exponential decay. The model is based on the asymptotic calculation of the Fourier integral, taking into account possible diffraction effects of the first and the second order.

Simulation framework for microwave SQUID multiplexer optimization

So far, performance prediction and optimization of microwave SQUID multiplexers have largely been based on simple approximate analytical models and experimental results. This is caused by the complexity of the underlying physics and the intricacy of operation and readout parameters. As a simplified description can never account for all potential effects occurring in a real device, we have developed a software framework to simulate the characteristics and performance of a microwave SQUID multiplexer. Our simulation framework is a powerful tool to guide understanding and optimization of microwave SQUID multiplexers and other related devices. It includes common readout schemes such as open-loop or flux ramp-modulated readout as well as the nonlinear behavior of Josephson tunnel junctions. Moreover, it accounts for the non-zero response time of superconducting microwave resonators with high loaded quality factors as well as the most significant noise contributions such as amplifier noise, resonator noise, as well as SQUID noise. This ultimately leads to a prediction of device performance that is significantly better compared to simple analytical methods. Using the simulation framework, we discuss first steps toward full microwave SQUID multiplexer optimization and highlight some other applications for which our simulation framework can be used.

Approximate models of air transport queueing systems with partial mutual assistance between service channels

Approximate analytical models are proposed for two types of multi-channel queuing systems with partial mutual assistance between channels and waiting in limited-size and unbounded queues. The incoming flow of requests is a superposition of several simplest flows. It is assumed that normative numbers of channels for servicing a customer that differ depending on the flow of incoming customer requests are established. In the systems of the first type the normative number of channels is not necessary: a customer is accepted for servicing if there are free channels in the system and the number of channels is smaller than the normative one. Service time is distributed exponentially with the average inversely proportional to the number of allocated channels. In systems of the second type the service of a customer is always performed by the channels of the normative number. Service time can be distributed arbitrarily (not only exponentially) with the average irrespective of the number of allocated channels. The paper presents the results of comparative analysis of the results of dealing with some tasks of designing service systems in a wide range of input data using simulation modelling and calculations based on approximate analytical models that allowed evaluating the application area of the latter and making a conclusion about their satisfactory accuracy. Examples of the use of models of technological processes of airport ground handling as queuing systems of the considered types are given.

Simultaneous electrostatic trapping of merged cation & anion beams.

Simultaneous trapping of merged cation and anion beams in the hybrid electrostatic ion beam trap (HEIBT) opens new opportunities for the study of the interactions of isolated atomic molecular or cluster ions with oppositely charged ionic species. Application of the trapped merged beams requires a detailed understanding of the trapping dynamics and the effect of the Coulombic attractive and repulsive forces between the ions on their motion in the trap. The simultaneous trapping regime is explored experimentally for SF6- anion and SF5+ cation beams and compared to realistic ion trajectory simulations. The respective stability of the simultaneously trapped cation and anion beams is experimentally tracked by nondestructive and mass sensitive image charge monitoring. An approximate analytical potential model is presented for modeling the dynamics of trapped ions, providing insight into the role of ion-ion interactions, and suggesting a simplified mirror design.

Approximate Analytical Model of Jet Flow with Mach Reflection and Pulsed Energy Supply at the Main Shock

Approximate Analytical Model of Jet Flow with Mach Reflection and Pulsed Energy Supply at the Main Shock

Use of the repeated integral transformation method to describe the transport of solute in soil

Predicting the fate and transport of contaminants in soil or groundwater systems using analytical or numerical models is crucial for environmental researchers. While the analytical models are a flexible approach to quantifying the subsurface contamination and remediation because they are non-susceptible to numerical dispersions, economical and handier; two-dimensional analytical models that describe a bilateral flow coupled with both sink and decay factors are rarely reported. Motivated by the case of a non-bare soil ridge with constant point-solute source lying internally but parallel to the longitudinal flow direction, a (2 + 1) dimensional Advection-Diffusion-Reaction Equation (ADRE) of bilateral flow coupled with the linear sorption, decay, and sink is formulated to model the transport of dissolved solute in a homogenous and isotropic non-fractured porous medium. Then, a brief review of exact and analytical methods for solving the ADRE is conducted to establish the right solution methods. The Repeated Integral Transformation Method (RITM) is employed to derive the approximate analytical solutions for the formulated model, maintaining the model's original terms for the efficient sensitivity analysis. The RITM uses Laplace and Fourier transforms with a wide range of computed results. We compare the approximate solutions with numerical simulations in COMSOL to verify the accuracy of the approximate analytical models. Then, the application of the solutions is demonstrated through a systematic analysis of the effect on solute transport of advection-diffusion, reaction, sorption, retardation, sink, and pore water velocity. Results show that the presence of sink, mimicked by plant-root uptake activity, and decay tend to reduce the solute concentration in the medium. While both the retardation and sorption factors affect the movement of the dissolved solutes, water content and pore-water velocity promote the spreading of dissolved solutes. Solute concentration in the medium increases at low Peclet numbers, signifying the influence of diffusive coefficients. The current proposed RITM-based solutions can characterize contamination in the soil, and should be useful to environmental researchers.

Random rough surface effects on the performance of near-field thermophotovoltaic system

Surfaces roughness exists inevitably during manufacturing process, while how it affects the performance of the near-field thermophotovoltaic (NF-TPV) system is still unclear. In this work, we investigate the effect of rough surfaces on the performance of NF-TPV systems theoretically. Two typical NF-TPV systems with the same plasmonic emitter (Ga-doped ZnO, GZO) and different TPV cells (GaSb and InAs) are considered. The effective multilayer approach and analytical approximation model are applied to analyze near-field radiative heat transfer and the performance of the NF-TPV system. Near-field radiative heat transfer between the ideal GZO and TPV cell with smooth surfaces is through the TR-SPPs modes (interaction between the evanescent waves generated by total reflection and the surface plasmon polaritons), while the surface roughness excites the red-shift and the coupling of the TR-SPPs modes. The influence of surface roughness on the performance of the NF-TPV system depends on the cooperation between the resonance frequency of the emitter and the bandgap of TPV cell. Generally, roughness increases the power output for a given average emitter-cell distance, while the efficiency can be improved or reduced. This work will help the understanding and evaluation of the performance of NF-TPV systems with rough surfaces.

Combination of Machine Learning and Analytical Correlations for Establishing Quantitative Compliance between the Trolox Equivalent Antioxidant Capacity Values Obtained via Electron Paramagnetic Resonance and Ultraviolet-Visible Spectroscopies.

Recent interest in the antioxidant capacity of foods and beverages is based on the established medical knowledge that antioxidants play an essential role in counteracting the damaging effects of free radicals, preventing human neurodegenerative diseases, cardiovascular disorders, and even cancer. At the same time, there is no “the method" that uniquely defines the antioxidant capacity of substances; moreover, the question of interrelation between results obtained by different experimental techniques is still open. In this work, we consider the trolox equivalent antioxidant capacity (TEAC) values obtained by electron paramagnetic resonance (EPR) spectroscopy and ultraviolet–visible (UV–vis) spectroscopy using the classic objects for such studies as an example: red, rosé, and white wine samples. Based on entirely different physical principles, these two methods give values that are not so simply interrelated; this creates a demand for machine learning as a suitable tool for revealing quantitative correspondence between them. The consideration consists of an approximate correlation-based analytical model for the key argument (i.e., ) with subsequent adjustment by machine learning-based processing utilizing the CatBoost algorithm with the usage of auxiliary chemical data, such as the total phenolic content and color index, which cannot be accurately described by analytical expressions.

A New Elastic Non Contacting Sealing Concept for Valves

The hydraulic binary counter concept was proposed as a means to realize compact and lightweight digital hydraulic cylinder drives for exoskeleton actuation. This counter principle is based on hydraulically actuated switching valves which have a hysteretic response with respect to the pilot pressure. Manufacturing tolerances of the tiny components caused unexpected high leakage which, in turn, led to a malfunction of the system.
 In this paper a new sealing concept, is introduced to solve this problem. It is based on a non-contact seal (sealing gap), which exploits a self-regulating, elasto-hydrodynamic effect to reduce a rather large initial gap h0 – to allow a rough tolerance – into a very small sealing gap h(x) to avoid dry friction of valve spool movement on the one hand but have very small leakage on the other hand.
 As sealing, an annular flexible ring made, e.g. of PTFE, is used which combines sufficient flexibility to allow this self adapting mechanism to a sufficient extent and to stay the high pressure loads.
 For the mathematical analysis of the concept, an approximate elasto-hydrodynamic analytical model is used. It sets the gap pressure, obtained from the Reynold’s equation for the sealing gap, the elastic restoring forces of the sealing ring, and the imparting pressure in equilibrium.
 The sealing concept is then simulated with a numerical model built with the finite element code ABAQUS, this results are compared with the one of the analytical model.
 It solves the Reynolds equation by a user defined subroutine. The simulation results indicate that this sealing principle delivers way better results than standard gap seals despite its rough manufacturing tolerances with one order of magnitude higher tolerance ranges. The application of this concept is not limited to small valves as needed for exoskeleton hydraulics but can be transferred to conventional type of hydraulics as well.

Analytical Solution of Heat Transfer Performance of Grid Regenerator in Inverse Stirling Cycle

The regenerator plays an extremely important role in the Stirling circulation. A grid regenerator can be used for inverse Stirling machines at room temperature due to its low flow resistance. This paper proposes a hexagonal grid regenerator to theoretically explore heat transfer properties in the inverse Stirling cycle and establishes an approximate analytical model to analyze the effect mechanism of working frequency, thermal diffusivity and wall thickness on the oscillation flow. The results show that the wall thickness is one of the key factors affecting the equivalent heat transfer coefficient. Specifically, too small or too large wall thickness increases the instability of the heat transfer process. The ultimate wall thickness is determined by the equivalent heat transfer coefficient and thermal penetration depth, whose optimal value ensures not only sufficient heat exchange but also the full utilization of materials. With the increase in frequency, heat exchange performance is improved monotonously. Therefore, high–frequency operation can improve the heat exchange performance of the regenerator. In addition, an optimization criterion for the size of regenerator with the specific capacity of heat transfer as the objective parameter is proposed based on the equivalent heat transfer coefficient. The optimal parameters were obtained when relative thickness was set as 0.8 mm and the equivalent heat transfer coefficient was up to 104–105 W/m2·K indicating that the grid regenerator has broad application prospects in the inverse Stirling cycle.

An Approximate Analytical Model of Surface Cracks in AC Field Measurement Technique

An appropriate modeling technique is critical for the quick analysis of alternating current (ac) field measurements destined for qualitative or quantitative studies of surface defects in conductive materials. Traditional modeling techniques often use the finite-difference method to solve the governing Laplace equation in the crack region, which gives a closed-form solution in the Fourier domain for regions outside the crack. However, these models are complex and only useful for cracks with extremely narrow openings. This article proposes an approximate analytical model that is based on current shunting of parallel circuits and the Biot–Savart law. We assume that the current induced by a high-frequency current-carrying coil is evenly distributed within a very thin layer at the surface of a conductor. In the presence of a defect, the current flows only along the edges and the bottom of the defect. Under these assumptions, the model simplifies the induced current by treating it as due to many current sources of equal amplitude. The magnetic field above the defect can be mathematically described by the linear superposition of these current sources. The proposed model can thus be used to analyze cracks with wider openings. We compare the magnetic-field signals of flat-bottomed cracks of various sizes as obtained by the proposed model and the finite-element method and also explore cracks with complex bottom profiles. The results show that the proposed model produces accurate quantitative and qualitative results for a wider range of defects.

Resistive electrode array (REA) for radiotherapy beam monitoring and quality assurance

We have developed a new type of detector array for monitoring of radiation beams in radiotherapy. The detector has parallel-plane architecture with multiple large-area uniform thin-film electrodes. At least one of the electrodes is resistive and has multiple signal readouts spread out along its perimeter. The integral dose deposited in the detector gives rise to multiple signals that depend on the distribution of radiation with respect to resistive electrode array (REA) geometry. The purpose of the present study was to experimentally determine basic detector response to MLC collimated x-ray fields. Two detector arrays have been characterized: circular and rectangular. The current and electrostatic potential distribution within the resistive electrode are governed by the Laplace and continuity equations with boundary conditions at the border with the readouts. Measurements for pencil beams showed that signal strength depends primarily on the distances between the location of the pencil beam and the readouts. Measurements for larger irregular MLC showed that signals as a function of time are quasi-linear with respect to MLC position and are proportional to the MLC area. Derivation of clinically relevant radiation beam parameters from REA signals, such as MLC position, MLC gap size and monitor unit per MLC segment relies on the detector response model with empirical model parameters. An approximate analytical detector response model was proposed and used to fit experiment data.

Theoretical analysis of close-contact melting on superhydrophobic surfaces

The present study deals with close-contact melting of a vertical cylinder on a horizontal isothermal superhydrophobic surface with an array of circular posts. A new numerical model for this phenomenon is formulated under several simplifying assumptions. For the limiting case of perfect slip and thermal contact, based on the model assumptions, it is demonstrated that superhydrophobic surfaces can enhance the melting time by no more than 30 %. Numerical solution of the new model reveals that the effect of superhydrophobic hydrodynamic slip can decrease the molten layer thickness. However, due to the dominant effect of thermal slip, the heat transfer rate can be decreased significantly, and the melting time can be roughly doubled. An approximate analytical model is developed for understanding the problem dynamics better. The analytical model predictions are compared extensively against the numerical model results. For sufficiently low surface volume fractions, the analytical model provides excellent estimations of the numerical model predictions. Dimensional analysis reveals that according to the analytical model, the ratio between the melting times for superhydrophobic and regular surfaces is governed by a single dimensionless group. Moreover, according to the analytical model, the melting time on a superhydrophobic surface is always longer than on a regular surface, which agrees qualitatively with the numerical model results. Based on this analysis, a dimensionless condition for the analytical model range of validity is formulated. Finally, a conservative criterion for the liquid–gas interface stability under a close-contact melting process is established.

Modeling and experiments of near-field thermophotovoltaic conversion: A review

This article provides an in-depth review of charge transport models utilized to analyze the performance of near-field thermophotovoltaic (NF-TPV) devices, and a comprehensive examination of NF-TPV experiments performed to date. Researchers have used several models to theoretically analyze NF-TPV devices; however, each model can result in different performances of NF-TPV devices, particularly due to characteristics of near-field thermal radiation. For clarification, we sort up-to-date analysis models into four categories; the analytical approximation model, detailed balance analysis, minority carrier separation (MCS) model, and Poisson-drift–diffusion (PDD) model. Key assumptions of each model are enumerated, and the calculated results by each model are compared. For the review of experimental works, we first sort NF-TPV experiments according to the manner of gap control into positioner-, spacer-, and MEMS-based approaches. Then, we introduce the primary design configuration of each approach and the compelling experimental results achieved by state-of-the-art studies. In addition, advanced concepts of hybrid devices and multi-junction PV cells, proposed to further improve NF-TPV performance, are briefly introduced. • A review of charge transport models used to analyze the NF-TPV device is provided. • Models are classified into analytical approximation, detailed balance, MCS, and PDD. • A comprehensive review of all NF-TPV experiments performed to date is conducted. • NF-TPV experiments are sorted into positioner-, spacer-, and MEMS-based approaches.

Modeling and Design of High-Power, High-Current-Ripple Planar Inductors

This article is focused on modeling and design optimization of high-current-ripple planar inductors in liquid-cooled high-power applications, such as electric-vehicle drivetrain systems, where efficiency and power density are the key performance metrics. The planar-inductor optimization is facilitated by innovations in computationally efficient and accurate models of ac winding loss and thermal management. A novel approximate analytical model for the ac winding loss takes into account effects of inside-the-core versus outside-the-core winding geometry as well as the air-gap fringing effect. Furthermore, thermal management strategies are introduced to enhance the vertical thermal flow from the core and the windings to the cold plate, leading to 2.5–3 times higher peak power capability compared with standard solutions. The developed modeling and optimization techniques are applied to planar inductor design in a 16.5-kW-rated SiC-based zero-voltage-switching quasi-square-wave boost converter, and the insights of selecting the core dimensions, number of turns and inductance are discussed in detail. The designed ELP 43-based planar inductor achieves a power density of 175.7 kW/L, and is experimentally validated on the converter prototype, achieving 98.8% efficiency at the typical 9.45-kW point, and less than 60 °C of worst-case temperature rise with a winding loss of 68 W in full power operation.

Experimental, Analytical and ANSYS Computation of Novel Cascade Solar Desalination Still

This study presents a simple device using solar radiation as a source of energy to convert brackish water to freshwater. To enhance the productivity of the cascade of solar stills, a new structure of the absorber plate with sloped surfaces and baffles was proposed to present a slight water layer thickness and improve the amount of solar radiation incident. A physical model is developed taking into account various parameters which affect the distillate yield of solar sills. In the present work, the modeling of the cascade solar still uses ANSYS Fluent V18 to investigate the yield. A three-dimensional model was considered to simulate the temperature of the water, absorber plate, and freshwater productivity. A comparison was conducted based on the CFD simulation results, experimental and approximate analytical model data. It showed a reasonable agreement of the results obtained using the analytical model with the experimental and the simulation using ANSYS Fluent of different working parameters especially the productivity. The best performance was obtained on 15/07/2018, with a productivity rate of more than 1.67 kg/m2.hr.

Analytic electrostatic model of amorphous-crystalline Ge2Sb2Te5 heterojunction

Motivated by its potential properties and applications, the energy band alignment of the amorphous-crystalline Ge2Sb2Te5 heterojunction in thermal equilibrium is explored. An approximate analytic model based on the exact solution to Poisson’s equation is constructed to describe the electrostatics of the heterojunction between the amorphous phase and the face-centred cubic crystalline phase of Ge2Sb2Te5. The model captures the physics of accumulation in the crystalline layer, as well as that of depletion and inversion due to the deep defect distribution in the amorphous layer. Without introducing fitting parameters, the model approximates the influence of the density of states parameters of each phase on the electric potential distribution across the heterojunction. It is then validated against the exact solution obtained numerically using solar cell capacitance simulations. Apart from the small inaccuracy in modelling the electric potential distribution in the depletion region, simulation results reveal that the approximations are successful in modelling the electrostatics of the heterojunction.

Approximate analytical model for transient transport and oxygen-limited biodegradation of vapor-phase petroleum hydrocarbon compound in soil

Volatile organic compounds (VOCs) contamination may occur in subsurface soil due to various reasons and pose great threat to people. Petroleum hydrocarbon compound (PHC) is a typical kind of VOC, which can readily biodegrade in an aerobic environment. The biodegradation of vapor-phase PHC in the vadose zone consumes oxygen in the soil, which leads to the change in aerobic and anaerobic zones but has not been studied by the existing analytical models. In this study, a one-dimensional analytical model is developed to simulate the transient diffusion and oxygen-limited biodegradation of PHC vapor in homogeneous soil. Laplace transformation and Laplace inversion of the Talbot method are adopted to derive the solution. At any given time, the thickness of aerobic zone is determined by the dichotomy method. The analytical model is verified against numerical simulation and experimental results first and parametric study is then conducted. The transient migration of PHC vapor can be divided into three stages including the pure aerobic zone stage (Stage I), aerobic-anaerobic zones co-existence stage (Stage II), and steady-state stage (Stage III). The proposed analytical model should be adopted to accommodate scenarios where the transient effect is significant (Stage II), including high source concentration, deep contaminant source, high biodegradation capacity, and high water saturation. The applicability of this model to determine the breakthrough time for better vapor intrusion assessment is also evaluated. Lower first-order biodegradation rate, higher source concentration, and shallower source depth all lead to smaller breakthrough time.

Angular correlations of causally-coherent primordial quantum perturbations

We consider the hypothesis that nonlocal, omnidirectional, causally-coherent quantum entanglement of inflationary horizons may account for some well-known measured anomalies of cosmic microwave background (CMB) anisotropy on large angular scales. It is shown that causal coherence can lead to less cosmic variance in the large-angle power spectrum C ℓ of primordial curvature perturbations on spherical horizons than predicted by the standard model of locality in effective field theory, and to new symmetries of the angular correlation function C(Θ). Causal considerations are used to construct an approximate analytic model for C(Θ) on angular scales larger than a few degrees. Allowing for uncertainties from the unmeasured intrinsic dipole and from Galactic foreground subtraction, causally-coherent constraints are shown to be consistent with measured CMB correlations on large angular scales. Reduced cosmic variance will enable powerful tests of the hypothesis with better foreground subtraction and higher fidelity measurements on large angular scales.

Analysis of static behavior of ion sensitive field effect Transistor for pH measurements

The Ion-Sensitive Field-Effect Transistor (ISFET) is one of the most popular pH sensors traditionally using to measure hydrogen ion concentration (pH) of the electrolytic solutions. It is developed from Metal Oxide Semiconductor Field-Effect Transistor (MOSFET) by replacing gate electrode with an electrolytic solution to be tested, and a reference metal electrode immersed in that solution. Basic principle of ISFET operation is based on that of standard NMOS structure in conjunction with the insulator-electrolyte capacitor as described in this paper. The site-binding theory (generalized to two kinds of binding sites), together with the Gouy-Chapman-Stern model for the potential profile in the electrolyte, is coupled to the MOS physics. As a result, an approximate analytical model which completely describes static behavior of the ISFET is obtained. The developed description can serve as useful tool for understanding many contemporary biosensors based on original ISFET structure which has broad application in bio-medicine, biological, chemistry and environmental areas.